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Sohel et al. Where, URec is the overall heat transfer coefficient, ARec is 2.5.2 Calculation of heat transfer coefficient of horizontal outside tubes The condenser tubes have circular fins attached to them. While calculating the total heat transfer from a finned tube, one must take into account the heat transfer through the fins as well. The weighted heat transfer coefficient for the finned tube is: αoAt =α(Afηf +Ar) (32) Where, Ar is the surface of the tube that is not covered by fins, Af is the surface of the fin and At is the total surface area, A =A +A. The fin efficiency, η for the the effective heat transfer area of the recuperator and the log mean temperature deference and calculated as: ∆tRec =(T4 −T2)−(T4a −T2') (27) m (T4 −T2) (T4a −T2') ln ∆tRec m is The value of the heat transfer coefficient is calculated using the following approximated equation: •• URec =URec(m2b/m2b,s)0.5 (28) • • standard heat transfer coefficient and m2b,s turbine outlet mass flow. 2.5 The condenser model Stfrf condenser tube is taken as 75%, which is a typical value. Here, m2b is the turbine outlet mass flow, URec S The average Nusselt number for a finned tube in a bank with a staggered tube arrangement with the number of rows less than 4 can be calculated using following equation Nu=0.19(ab)0.2(ds)0.18(dh)−0.14 Re0.65 Pr0.33 Where, a=s1 /d, b=s2 /d, s1, s2 are transverse and longitudinal bank pitch, and s is fin spacing. This equation is valid in the range 102< Re <2 X 104. is the is the standard (33) The ORC unit uses an air-cooled condenser. The following equation is used to calculate the outlet enthalpy: h =h −Qcon (29) 14• αd m2b Modelling assumptions for the condenser are listed below: • The mass flow rate is conserved. • The minimum temperature of the condenser is 7°C more than the saturated temperature of the pentane at the prevailing pressure in the condenser. • There is a minimum temperature difference of 8°C between the ambient temperature and the condenser outlet temperature to provide heat transfer from the pentane to the ambient air. • Lumped heat capacity method was used for the calculation. The calculated Biot number of the fins is 8.4 X 10-6 . It is much less than 0.1, the criterion for such analysis (Holman 1992). 2.5.1 Calculation of heat transfer coefficient of horizontal inside tubes The equations used to model heat transfer coefficients are taken from (Mueller 1992). The equation for heat transfer coefficient is calculated from the following equation of horizontal tubes assuming a stratified layer: Nu= k (34) and Re = ρwd (35) η Where d is the tube diameter at the fin base and w is the maximum velocity of the fluid, which occurs at the minimum free cross section of the finned-tube bank (Figure 7). Figure 7: Definitions of quantities for flow in finned-tube banks. ⎡k3ρ (ρ −ρ )g∆h ⎤1/4 αi=Ω⎢lll g v⎥ ⎣ ηldi(Tsat −Tw) ⎦ (30) Where, ρl is the density of fluid at a liquid state, ρg is the density of fluid at a vapour state, ηl is the dynamic viscosity, Tsat is the saturation temperature, Tw and ∆hv is the change in enthalpy. is the wall temperature (31) ⎡ 1−x ρ 23⎤ Ω=0.728⎢1+( g)( g)⎥−3/4 ⎢ xg ρl⎥ ⎣⎦ 6PDF Image | Dynamic Modelling and Simulation of an Organic Rankine Cycle Unit of a Geothermal Power Plant
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